Research on non-cognitive factors has shown that persistence in the face of challenges plays an important role in learning. However, recent work on wheel-spinning, a type of unproductive persistence where students spend too much time struggling without achieving mastery of skills, show that not all persistence is uniformly beneficial for learning.…

We present a reconceptualized framework for opportunity to learn (OTL) in school mathematics that builds on previous conceptualizations of OTL and includes features related to both quantity (i.e., time) and quality. Our framework draws on existing literature and on our own observational research of mathematics teaching practices. Through the…

The accepted framing of mathematics pedagogical content knowledge (PCK) as part of mathematical knowledge for teaching has centered on the question: What mathematical reasoning, insight, understanding, and skills are required for a person to teach elementary mathematics? Many have worked to address this question in K-8 teaching. Yet, there remains…

Math coaches play a vital role in strengthening math instruction and learning in schools. However, without a collegial relationship with the teachers they are trying to help, it is difficult to foster productive collaborations that lead to better teaching practice and increased student achievement. This resource helps coaches confidently clarify,…

This book provides a landscape of learning that helps teachers recognize, support, and celebrate their students' capacity to structure their worlds algebraically. It identifies the models, contexts, and landmarks that facilitate algebraic thinking in young students and provides insightful and practical methods for teachers, math supervisors, and…

This article draws on Lefebvre's rhythmanalysis to interrogate and extend Bernstein's theory of pedagogic framing. It develops a typology of modes of pedagogic practice differentiated in terms of the dominance of one of three potential organising referents. These are (a) the grammar of the instructional discourse configured by a regulative…